Two children are playing on stools at a restaurant counter. Their feet do not reach the footrests, and the tops of the stools are free to rotate without friction on pedestals fixed to the floor. One of the children catches a tossed ball, in a process described by the equation
(a) Solve the equation for the unknown
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Physics for Scientists and Engineers
- A space probe, initially at rest, undergoes an internal mechanical malfunction and breaks into three pieces. One piece of mass ml = 48.0 kg travels in the positive x-direction at 12.0 m/s, and a second piece of mass m2 = 62.0 kg travels in the xy-plane at an angle of 105 at 15.0 m/s. The third piece has mass m3 = 112 kg. (a) Sketch a diagram of the situation, labeling the different masses and their velocities, (b) Write the general expression for conservation of momentum in the x- and y-directions in terms of m1, m2, m3, v1, v2 and v3 and the sines and cosines of the angles, taking to be the unknown angle, (c) Calculate the final x-components of the momenta of m1 and m2. (d) Calculate the final y-components of the momenta of m1 and m2. (e) Substitute the known momentum components into the general equations of momentum for the x- and y-directions, along with the known mass m3. (f) Solve the two momentum equations for v3 cos and v3 sin , respectively, and use the identity cos2 + sin2 = 1 to obtain v3. (g) Divide the equation for v3 sin by that for v3 cos to obtain tan , then obtain the angle by taking the inverse tangent of both sides, (h) In general, would three such pieces necessarily have to move in the same plane? Why?arrow_forwardAs shown in Figure P8.20, a bullet of mass m and speed v passes completely through a pendulum bob of mass M. The bullet emerges with a speed of v/2. The pendulum bob is suspended by a stiff rod (not a string) of length , and negligible mass. What is the minimum value of v such that the pendulum bob will barely swing through a complete vertical circle? Figure P8.20arrow_forwardA space probe is fired as a projectile from the Earths surface with an initial speed of 2.00 104 m/s. What will its speed be when it is very far from the Earth? Ignore atmospheric friction and the rotation of the Earth. P11.26 Ki+Ui=Kf+Uf12mvi2+GMEm(1rf1ri)=12mvf212vi2+GME(01RE)=12vf2orvf2=v122GMEREandvf=(v122GMERE)1/2,vf=[(2.00104)21.25108]1/2m/s=1.66104m/sarrow_forward
- A rocket has total mass Mi = 360 kg, including Mfuel = 330 kg of fuel and oxidizer. In interstellar space, it starts from rest at the position x = 0, turns on its engine at time t = 0, and puts out exhaust with relative speed ve = 1 500 m/s at the constant rate k = 2.50 kg/s. The fuel will last for a burn time of Tb = Mfuel/k = 330 kg/(2.5 kg/s) = 132 s. (a) Show that during the burn the velocity of the rocket as a function of time is given by v(t)=veln(1ktMi) (b) Make a graph of the velocity of the rocket as a function of time for times running from 0 to 132 s. (c) Show that the acceleration of the rocket is a(t)=kveMikt (d) Graph the acceleration as a function of time. (c) Show that the position of the rocket is x(t)=ve(Mikt)ln(1ktMi)+vet (f) Graph the position during the burn as a function of time.arrow_forwardA particle of mass 0.303 kg and another of mass 0.697 kg are connected by a rigid, massless rod 0.410 m long. The structure rotates at 11.1 rad/s about an axis perpendicular to the rod and passing through the center of mass of the two particles. How much is the kinetic energy of rotation (in Joules)? Choose an option : a) 1,53 b) 0,437 c) 3,72 d) 2,19 e) 4,37 f) 3,28 g) 1,09 h) 2,62arrow_forwardIn the figure, two satellites, A and B, both of mass m = 49.1 kg, move in the same circular orbit of radius r = 7410 km around Earth (mass ME = 5.98×1024 kg) but in opposite senses of rotation and therefore on a collision course. (a) Find the total mechanical energy EA+ EB of the two satellites + Earth system before the collision. (b) If the collision is completely inelastic so that the wreckage remains as one piece of tangled material (mass = 2m), find the total mechanical energy immediately after the collision. (c) Just after the collision, is the wreckage falling directly toward Earth’s center or orbiting around Earth?arrow_forward
- Three masses are placed on the x-axis : 300 g at origin, 500 g at x = 40 cm and 400 g at x = 70 cm. Thedistance of the centre of mass from the origin is -(1) 45 cm (2) 50 cm (3) 30 cm (4) 40 cmarrow_forwardCalculate the magnitude of the linear momentum for the following cases. (a) a proton with mass 1.67 10-27 kg, moving with a speed of 4.00 106 m/s (b) a 18.0-g bullet moving with a speed of 470 m/s kg · m/s(c) a 80.0-kg sprinter running with a speed of 10.0 m/s kg · m/s(d) the Earth (mass = 5.98 1024 kg) moving with an orbital speed equal to 2.98 104 m/s. kg · m/sarrow_forwardCalculate the magnitude of the linear momentum for the following cases. (a) a proton with mass 1.67 10-27 kg, moving with a speed of 4.10 106 m/skg · m/s(b) a 13.0-g bullet moving with a speed of 435 m/skg · m/s(c) a 71.0-kg sprinter running with a speed of 11.0 m/skg · m/s(d) the Earth (mass = 5.98 1024 kg) moving with an orbital speed equal to 2.98 104 m/s.kg · m/sarrow_forward
- Calculate the magnitude of the linear momentum for the following cases. (a) a proton with mass 1.67 10-27 kg, moving with a speed of 5.75 106 m/s kg · m/s(b) a 13.5-g bullet moving with a speed of 485 m/s kg · m/s(c) a 73.0-kg sprinter running with a speed of 11.0 m/s kg · m/s(d) the Earth (mass = 5.98 1024 kg) moving with an orbital speed equal to 2.98 104 m/s.arrow_forwardTwo masses m1 = 15 kg amd m2 = 25 kg are joined by connecting a rod of length 0.8 m. Determine the distance of the CM of the system from the m1 if a.) the connecting rod is massless, and b.) the connecting rod is a uniform rod of mass 15 kgarrow_forwardCalculate the magnitude of the linear momentum for the following cases. (a) a proton with mass 1.67 x 10-27 kg, moving with a speed of 4.60x106 m/s(b) a 12.0-g bullet moving with a speed of 290 m/s (c) a 77.0-kg sprinter running with a speed of 11.5 m/s(d) the Earth (mass = 5.98 x 1024 kg) moving with an orbital speed equal to 2.98 x 104 m/s.arrow_forward
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